# operator+,-,*,/ (std::complex)

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< cpp‎ | numeric‎ | complex

| (1) |
template< class T > std::complex<T> operator+( const std::complex<T>& lhs, const std::complex<T>& rhs ); |  | (until C++20)
template< class T > constexpr std::complex<T> operator+( const std::complex<T>& lhs, const std::complex<T>& rhs ); |  | (since C++20)
| (2) |
template< class T > std::complex<T> operator+( const std::complex<T>& lhs, const T& rhs ); |  | (until C++20)
template< class T > constexpr std::complex<T> operator+( const std::complex<T>& lhs, const T& rhs ); |  | (since C++20)
| (3) |
template< class T > std::complex<T> operator+( const T& lhs, const std::complex<T>& rhs ); |  | (until C++20)
template< class T > constexpr std::complex<T> operator+( const T& lhs, const std::complex<T>& rhs ); |  | (since C++20)
| (4) |
template< class T > std::complex<T> operator-( const std::complex<T>& lhs, const std::complex<T>& rhs ); |  | (until C++20)
template< class T > constexpr std::complex<T> operator-( const std::complex<T>& lhs, const std::complex<T>& rhs ); |  | (since C++20)
| (5) |
template< class T > std::complex<T> operator-( const std::complex<T>& lhs, const T& rhs ); |  | (until C++20)
template< class T > constexpr std::complex<T> operator-( const std::complex<T>& lhs, const T& rhs ); |  | (since C++20)
| (6) |
template< class T > std::complex<T> operator-( const T& lhs, const std::complex<T>& rhs ); |  | (until C++20)
template< class T > constexpr std::complex<T> operator-( const T& lhs, const std::complex<T>& rhs ); |  | (since C++20)
| (7) |
template< class T > std::complex<T> operator*( const std::complex<T>& lhs, const std::complex<T>& rhs ); |  | (until C++20)
template< class T > constexpr std::complex<T> operator*( const std::complex<T>& lhs, const std::complex<T>& rhs ); |  | (since C++20)
| (8) |
template< class T > std::complex<T> operator*( const std::complex<T>& lhs, const T& rhs ); |  | (until C++20)
template< class T > constexpr std::complex<T> operator*( const std::complex<T>& lhs, const T& rhs ); |  | (since C++20)
| (9) |
template< class T > std::complex<T> operator*( const T& lhs, const std::complex<T>& rhs ); |  | (until C++20)
template< class T > constexpr std::complex<T> operator*( const T& lhs, const std::complex<T>& rhs ); |  | (since C++20)
| (10) |
template< class T > std::complex<T> operator/( const std::complex<T>& lhs, const std::complex<T>& rhs ); |  | (until C++20)
template< class T > constexpr std::complex<T> operator/( const std::complex<T>& lhs, const std::complex<T>& rhs ); |  | (since C++20)
| (11) |
template< class T > std::complex<T> operator/( const std::complex<T>& lhs, const T& rhs ); |  | (until C++20)
template< class T > constexpr std::complex<T> operator/( const std::complex<T>& lhs, const T& rhs ); |  | (since C++20)
| (12) |
template< class T > std::complex<T> operator/( const T& lhs, const std::complex<T>& rhs ); |  | (until C++20)
template< class T > constexpr std::complex<T> operator/( const T& lhs, const std::complex<T>& rhs ); |  | (since C++20)

Implements the binary operators for complex arithmetic and for mixed complex/scalar arithmetic. Scalar arguments are treated as complex numbers with the real part equal to the argument and the imaginary part set to zero.

1-3) Returns the sum of its arguments.
4-6) Returns the result of subtracting rhs from lhs.
7-9) Multiplies its arguments.
10-12) Divides lhs by rhs.

### Parameters

lhs, rhs | - | the arguments: either both complex numbers or one complex and one scalar of matching type (float, double, long double)

### Return value

1-3) std::complex<T>(lhs) += rhs
4-6) std::complex<T>(lhs) -= rhs
7-9) std::complex<T>(lhs) *= rhs
10-12) std::complex<T>(lhs) /= rhs

### Notes

Because template argument deduction does not consider implicit conversions, these operators cannot be used for mixed integer/complex arithmetic. In all cases, the scalar must have the same type as the underlying type of the complex number.

The GCC flag "-fcx-limited-range" (included by "-ffast-math") changes the behavior of complex multiply/division by removing checks for floating point edge cases. This impacts loop vectorization.

### Example

Run this code

    #include <complex>
    #include <iostream>

    int main()
    {
        std::complex<double> c2(2.0, 0.0);
        std::complex<double> ci(0.0, 1.0);

        std::cout << ci << " + " << c2 << " = " << ci + c2 << '\n'
                  << ci << " * " << ci << " = " << ci * ci << '\n'
                  << ci << " + " << c2 << " / " << ci << " = " << ci + c2 / ci << '\n'
                  << 1  << " / " << ci << " = " << 1.0 / ci << '\n';

    //    std::cout << 1.0f / ci; // compile error
    //    std::cout << 1 / ci; // compile error
    }

Output:

    (0,1) + (2,0) = (2,1)
    (0,1) * (0,1) = (-1,0)
    (0,1) + (2,0) / (0,1) = (0,-1)
    1 / (0,1) = (0,-1)

### See also

operator+=operator-=operator*=operator/= | compound assignment of two complex numbers or a complex and a scalar (public member function)
operator+operator- | applies unary operators to complex numbers (function template)

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